Question: Is ${201532}$ divisible by $4$ ?
Answer: A number is divisible by $4$ if the last two digits are divisible by $4$ . [ Why? We can rewrite the number as a multiple of $100$ plus the last two digits: $ \gray{2015} {32} = \gray{2015} \gray{00} + {32} $ Because $201500$ is a multiple of $100$ , it is also a multiple of $4$ So as long as the value of the last two digits, ${32}$ , is divisible by $4$ , the original number must also be divisible by $4$ Is the value of the last two digits, $32$ , divisible by $4$ Yes, ${32 \div 4 = 8}$, so $201532$ must also be divisible by $4$.